\(n(r)\)  represents the mean number of particles \(j\)  in a spherical
shell of radius \(r\)  and thickness \(\Delta r\)  centered on particle
\(i\) . Finally, an average of \(g(r)\)  over all \(N\)  particle \(i\)  of the
simulation box is performed. Integrating \(4\pi r^2\rho g(r)\) , with
\(\rho =N/V\)  up to the first minimum \(g(r)\)  gives access to the mean
coordination number. Figure REF  displays the curves of
\(g(r)\)  from \(NVT\)  simulations. For all the thermodynamic states an
excellent match with AIMD simulations is seen. A quantitative
estimation of the departure was obtained by calculating the MSE
between the classical MD and AIMD curves for each temperature. The
MSE ranges from \(6^{-4}\)  typically in the case of the liquid states tot
\(1.2\times 10^{-2}\)  in the case of fcc solid states. The larger MSE
for the solid might come from the fact that even a very small
position shift of \(g(r)\)  can induce a significant departure as peaks
are sharp and narrow. Comparison with existing experiments was
already done in our previous work [1]} and is not
repeated here due to the very good agreement found here. This is
all the more true for the average coordination numbers with a
departure that does not exceed \(0.2\)  (see Table REF ). A
comparison with the most widely used EAM [2]} and
MEAM [3]} potentials is shown in Fig. S1 in the Supplementary
Information File for the same thermodynamic states. They are shown
to perform less well than the HDNN potential, as assessed by a
\(t\) -statistics, and especially for the high pressures.
<FIGURE><TABLE>